1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dafna1 [17]
3 years ago
12

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1

z − 2.

Mathematics
1 answer:
charle [14.2K]3 years ago
8 0

<u>Answer-</u> Length of the curve of intersection is 13.5191 sq.units

<u>Solution-</u>

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t   (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ \frac{dx}{dt} = -\sin t

  \frac{dy}{dt} = 2 \cos t

  \frac{dz}{dt} = \sin t-2cos t

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

∴ Arc length

= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}

=\int_{0}^{2\pi}\sqrt{(-\sin t)^{2}+(2\cos t)^{2}+(\sin t-2\cos t)^{2}

=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)

Now evaluating the integral using calculator,

=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t) = 13.5191




You might be interested in
I’m confused on the type of angles these are and how to solve them . (Parallel lines and Transversals)
svp [43]

Answer:

7) 49°

8) 77°

9) 87°

10) 135°

Step-by-step explanation:

7) The angles are between the parallel lines, so are "interior." They are on opposite sides of the transversal, so are "opposite interior" angles. Such angles are congruent, so ...

... ? ≅ 49°

8) The angles are adjacent interior angles, so are supplementary.

... ? + 103° = 180°

... ? = 77°

9) The angles are outside the parallel lines, so are "exterior." They are on opposite sides of the transversal, so are "opposite exterior" angles. Such angles are congruent.

... ? ≅ 87°

10) These are vertical angles, so are congruent. (The other parallel line is irrelevant and doesn't need to be there for this relationship to be true.)

... ? ≅ 135°

4 0
3 years ago
Which number is not the same type of number as the others in the list? 5.85, 63.4, 8.52624, 27.5
Darya [45]

8.52624 is not the same as 5.85, 63.4 , and 27.5.

Hope this Helps!!

6 0
3 years ago
Read 2 more answers
Forty percent of the 30 members of the drama club were members of the senior class
andriy [413]

10%of30=3

3x4=12

A. 40%of 30=12 senior class members.

B. 60% of the class were not senior class members

4 0
2 years ago
Read 2 more answers
A particular telephone number is used to receive both voice calls and fax messages. suppose that 20% of the incoming calls invol
Phoenix [80]

Answer:

0.1091 or 10.91%

Step-by-step explanation:    

We have been given that a particular telephone number is used to receive both voice calls and fax messages. suppose that 20% of the incoming calls involve fax messages and consider a sample of 20 calls. We are asked to find the probability that exactly 6 of the calls involve a fax message.  

We will use Bernoulli's trials to solve our given problem.

P(X=x)=^nC_x\cdot P^x(1-P)^{n-x}

P(X=6)=^{20}C_6\cdot (0.20)^6(1-0.20)^{20-6}

P(X=6)=\frac{20!}{6!(20-6)!}\cdot (0.20)^6(0.80)^{14}

P(X=6)=\frac{20!}{6!(14)!}\cdot (0.000064)(0.04398046511104)

P(X=6)=38760\cdot (0.000064)(0.04398046511104)

P(X=6)=0.1090997009730

P(X=6)\approx 0.1091\\

Therefore, the probability that exactly 6 of the calls involve a fax message would be approximately 0.1091 or 10.91%.

4 0
3 years ago
What is 83.03 plus 5percent equals to what
kati45 [8]
♥ 5%= 0.05
83.03+0.05=<span>83.08
Final answer: </span>83.08
5 0
3 years ago
Other questions:
  • What is the formula to calculate surface area of a triangular prism?
    13·2 answers
  • Find the measure of Angle 1
    5·2 answers
  • The question is in the figure below.
    6·1 answer
  • A machine packs 2/5 of a box every 1/2 minute. What is the number of boxes per minute packed? Why?
    15·1 answer
  • A gym charges a one-time fee of $75 to join, plus membership dues of $25 per month. Which equation represents the total cost, C,
    13·2 answers
  • Thank you to whoever helps me. I'm confused a little bit.
    13·1 answer
  • Find the probability of choosing a penny or a dime from 4 pennies 3 nickeles and 6 dimes
    9·2 answers
  • 1st correcct will get brainliest
    7·1 answer
  • Select the correct answer.
    5·1 answer
  • The graph of the absolute value parent function, f(x) = |x|, is stretched horizontally by a factor of 6 to create the graph of g
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!